Which set of numbers is a Pythagorean triple?
A. 4,5,6
B. 8,15,17
C. 5,12,14
D. 8,24,25
To determine which set of numbers is a Pythagorean triple, we need to see if they satisfy the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Let's check each option:
A. 4, 5, 6:
4^2 + 5^2 = 16 + 25 = 41
6^2 = 36
Since 41 is not equal to 36, A is not a Pythagorean triple.
B. 8, 15, 17:
8^2 + 15^2 = 64 + 225 = 289
17^2 = 289
Since 289 is equal to 289, B is a Pythagorean triple.
C. 5, 12, 14:
5^2 + 12^2 = 25 + 144 = 169
14^2 = 196
Since 169 is equal to 196, C is not a Pythagorean triple.
D. 8, 24, 25:
8^2 + 24^2 = 64 + 576 = 640
25^2 = 625
Since 640 is not equal to 625, D is not a Pythagorean triple.
Therefore, the set of numbers that is a Pythagorean triple is B. 8, 15, 17.
To determine which set of numbers is a Pythagorean triple, we need to check if they satisfy the Pythagorean theorem. The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Let's test each of the given sets of numbers:
A. 4, 5, 6:
4^2 + 5^2 = 16 + 25 = 41, which is not equal to 6^2 (36). Therefore, this set of numbers is not a Pythagorean triple.
B. 8, 15, 17:
8^2 + 15^2 = 64 + 225 = 289, which is equal to 17^2 (289). Therefore, this set of numbers is a Pythagorean triple.
C. 5, 12, 14:
5^2 + 12^2 = 25 + 144 = 169, which is equal to 13^2 (169). Therefore, this set of numbers is a Pythagorean triple.
D. 8, 24, 25:
8^2 + 24^2 = 64 + 576 = 640, which is not equal to 25^2 (625). Therefore, this set of numbers is not a Pythagorean triple.
Based on the Pythagorean theorem, the sets of numbers that form Pythagorean triples are B. 8, 15, 17, and C. 5, 12, 14.
a^2 + b^2 = c^2
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